Chapter 25__upload_Genetics of Populations

True regardless of starting allele frequencies hardy

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Unformatted text preview: as the alleles Three possible diploid genotypes AA, Aa, aa Frequency of allele A is called p Frequency of allele a is called q p+q=1 (note: we could have called a=p and A=q, no difference!) Hardy-Weinberg Equilibrium Principle Principle The General Case: Let gametes make zygotes: Four combinations A + A = AA p X p = p2 A + a = Aa p X q = pq a + A = aA q X p = qp a + a = aa q X q = q2 p2 + 2pq + q2 = 1 Genotype frequencies in Hardy-Weinberg Equilibrium Hardy-Weinberg Equilibrium Principle Principle Two fundamental conclusions: Conclusion 1: the allele frequencies in a population will not change, generation after generation (given our assumptions) Conclusion 2: if the allele frequencies in a population are given by p and q, the genotype frequencies will be given by p2, 2pq, and q2 Hardy-Weinberg Equilibrium Principle Principle Why do we use Hardy-Weinberg Equilibrium Principle? • Shows evolution is not happening • Gives specific set of testable assumptions • If an assumption is violated, the Conclusions do not hold • Is a null model with which to test for evolution!!!! The Hardy-Weinberg principle Given certain assumptions, whatever the initial genotype frequencies for two autosomal alleles may be, after one generation of random mating, the genotype frequencies will be p2:2pq:q2, and both the genotype frequencies and the allele frequencies will remain constant in succeeding generations. HWE in Action… HWE p +q=1 (p + q)2 = 12 p2 + 2pq + q2 = 1 f(A) f(a) f(A) f(AA) = f(A) x f(A) f(aA) = f(a) x f(A) p2 = f(AA) pq + pq = 2pq = f(Aa) q2 = f(aa) f(a) f(Aa) = f(A) x f(a) f(aa) = f(a) x f(a) What is HWE good for? What Estimations of Allele or Genotype Frequencies: • Predicting genotype frequencies given allele frequencies • Genotypes will approximate a binomial distribution – (p + q)2 = 1 after 1 generation of random mating. • If we know the allele frequencies in generation 1, we can predict the genotype frequencies in generation 2. • Allele and genotype frequencies will not change as long as the assumptions are met. For example: For Generation 1: – f(AA) = 0.2, f(Aa) = 0.8, f(aa) = 0.0 What are the genotype frequencies in generation 2? First, find p and q: – p = 0.2 + (0.8 / 2) = 0.6 – q = 0.0 + (0.8 / 2) = 0.4 Generation 2: – F(AA) = p2 = 0.36 – F(Aa) = 2pq = 0.48 – F(aa) = q2 = 0.16 Another example: Another Generation 1: – f(AA) = 0.5, f(Aa) = 0.2, f(aa) = 0.3 What are the genotype frequencies in generation 2? First, find p and q: – p = 0.5 + (0.2 / 2) = 0.6 – q = 0.3 + (0.2 / 2) = 0.4 Generation 2: – F(AA) = p2 = 0.36 – F(Aa) = 2pq = 0.48 – F(aa) = q2 = 0.16 Did you notice? Did We started with different genotype frequencies in each example, but the same allele frequencies (p & q). We ended (generation 2) with the same genotype frequencies in both examples. If all of the assumptions are met, what will be the genotype frequencies in generation 10? What else is HWE good for? for? Null hypothesis: – H0: th...
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